I am the author and maintainer of the Data Layer Manager and AA Product String Builder extensions. You are very close to seeing this configuration working. There are just two things that I need you to verify.
1). Please verify that the data element that is providing "Data Layer Root" is a DLM Context Aware data element and is configured like this (note that the Data Layer Path field is left empty):
2) The Product Collection Path should be set to the string "product" as below:
Everything else about your configuration looks just fine. Please reply to let me know if this solved your issue.